Persistent Homology and String Vacua

TL;DR

This paper applies topological data analysis to study the distribution and topological features of various string vacua, aiming to characterize their physical properties through persistent homology.

Contribution

It introduces the novel application of topological data analysis to string theory vacua, providing new insights into their topological and physical structure.

Findings

Identified persistent topological features in distributions of Calabi-Yau and Landau-Ginzburg models.

Extracted physical information from flux compactifications using topological methods.

Characterized phenomenologically realistic heterotic models through their topological properties.

Abstract

We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by identifying which homological characteristics persist over a long range of scales. We apply these techniques in several contexts. We analyze N=2 vacua by focusing on certain distributions of Calabi-Yau varieties and Landau-Ginzburg models. We then turn to flux compactifications and discuss how we can use topological data analysis to extract physical informations. Finally we apply these techniques to certain phenomenologically realistic heterotic models. We discuss the possibility of characterizing string vacua using the topological properties of their distributions.